Inflation is a well motivated paradigm which makes a number of non–trivial predictions which have been found to be in agreement with a variety of cosmological observations. In particular it is in agreement with measurements of anisotropies in the cosmological microwave background (CMB) radiation [1]} and the fact that the universe is spatially nearly flat. Importantly, it provides a self-consistent causal explanation for the origin of large scale structures (galaxies & clusters of galaxies) via quantum fluctuations that are stretched to cosmological scales, providing the seeds for structure formation [2]}. Inflation was proposed as a mechanism to relieve initial condition problems that arose with the original Hot Big Bang model. Despite curing these initial conditions problems, the theory of inflation still depicts a universe originating from a singular point [3]}, [4]}Assuming the validity of General Relativity (GR).. The idea of replacing the singular origin, the Big Bang, with a non-singular transition, a bounce, is not a new one and we refer to extensive reviews on this topics, such as e.g. [5]}, [6]}, [7]}. A model with a single bounce does not necessarily cure the initial condition (or singularity) problem, but simply pushes the solution back to an earlier state. Many different types of cosmological bouncing models have been proposed, e.g. using extra dimensions and branes [8]}, [9]}, [10]}, [11]}, [12]}, modifications to gravity or the kinetic terms [13]}, [14]}, [15]}, [16]}, or simply arising as a fundamental starting point in quantum cosmologies [17]}. One of the early attempts at avoiding the initial singularity was presented in [18]}, by considering a closed Robertson-Walker geometry. They found that a violation of the energy conditions due to the quantum effects in their model results in a transition from a Friedmann-like collapse to a Friedmann-like expansion. However, in their solution the universe will eventually collapse after completing a cycle, and their model cannot show if quantum effects would always avoid a gravitational collapse. Many of these models propose an alternative to inflation and aim to predict the observed anisotropies of the CMB within these alternative scenarios [19]}, [20]}, [21]}. Unfortunately, many alternatives to inflation will suffer from a fine-tuning problem, due to instabilities in the energy components driving the bounce. Nevertheless, these models provide a starting point to formulate a more complete theory of the universe, e.g. in which the universe undergoes cycles.
